Need to know how to do this problem

Question

If       and      , find the following:

      +  

     +  

      +  

    +  

Answer 1

Remember that i = √(-1)

Adding and subtracting is simple---just add the like terms.

Example: 3 - 2i + (5 +3i) = 8 + i

To multiply, use the same procedure as if i were something like or y

(5 + i) * (4 - i) =

20 -i i -i²

but i² = -1, so

20 - i +1

21 - i

Answer 2

(2+3i) + (4-5i) = (2+3) + (3-5)i = 5 - 2i

(2+3i) - (4-5i) = (2-4) + (3-(-5))i = -2 + 8i

(2+3i)(4-5i) = 8 - 10i + 12i - 15i² = 23+2i (Recall: i² = -1)

(2+3i) / (4-5i) = [(2+3i)(4+5i)] / [(4-5i)(4+5i)] = (8 +10i + 12i + 15i²) / (16 - 25i²) = (-7 + 22i) / 41

= (-7/41) + (22/41)i